We may begin the study of the polarization of light, with ease and profit, by means of a crystal of tourmaline.  But we must start with a clear conception of an ordinary beam of light.  It has been already explained that the vibrations of the individual ether-particles are executed across the line of propagation.  In the case of ordinary light we are to figure the ether-particles as vibrating in all directions, or azimuths, as it is sometimes expressed, across this line.

Now, in the case of a plate of tourmaline cut parallel to the axis of the crystal, a beam of light incident upon the plate is divided into two, the one vibrating parallel to the axis of the crystal, the other at right angles to the axis.  The grouping of the molecules, and of the ether associated with the molecules, reduces all the vibrations incident upon the crystal to these two directions.  One of these beams, namely, that whose vibrations are perpendicular to the axis, is quenched with exceeding rapidity by the tourmaline.  To such vibrations many specimens of the crystal are highly opaque; so that, after having passed through a very small thickness of the tourmaline, the light emerges with all its vibrations reduced to a single plane.  In this condition it is what we call plane polarized light.

[Illustration:  Fig. 27.]

[Illustration:  Fig. 28.]

A moment’s reflection will show that, if what is here stated be correct, on placing a second plate of tourmaline with its axis parallel to the first, the light will pass through both; but that, if the axes be crossed, the light that passes through the one plate will be quenched by the other, a total interception of the light being the consequence.  Let us test this conclusion by experiment.  The image of a plate of tourmaline (t t, fig. 27) is now before you.  I place parallel to it another plate (t’ t’):  the green of the crystal is a little deepened, nothing more; this agrees with our conclusion.  By means of an endless screw, I now turn one of the crystals gradually round, and you observe that as long as the two plates are oblique to each other, a certain portion of light gets through; but that when they are at right angles to each other, the space common to both is a space of darkness (fig. 28).  Our conclusion, arrived at prior to experiment, is thus verified.

Let us now return to a single plate; and here let me say that it is on the green light transmitted by the tourmaline that you are to fix your attention.  We have to illustrate the two-sidedness of that green light, in contrast to the all-sidedness of ordinary light.  The white light surrounding the green image, being ordinary light, is reflected by a plane glass mirror in all directions; the green light, on the contrary, is not so reflected.  The image of the tourmaline is now horizontal; reflected upwards, it is still green; reflected sideways, the image is reduced to blackness, because of the incompetency of